Variables Selection In Joint Model Via Adaptive Lasso

We consider the question about the variables selection in the joint model which is applied to deal with the survival data and longitudinal data. We focus on three things in the paper. First of all, we want to know the relationship between the time-to-event variable and the longitudinal output variable. Moreover, we are interested in selecting the significant variables and omitting the insignificant variables in the joint model. The method proposed in this paper can satisfy the three points. As for longitudinal data, we build the linear mixed effect model which is used to estimate the coefficients by maximizing the penalized likelihood function with the adaptive lasso penalty. The selection criterion of penalty parameters is based on ICQ criterion in the paper. As for time-to-event data, we build the proportional hazards model. In this model, we try to estimate the coefficient by maximizing the partial penalized likelihood function with the adaptive lasso penalty.Thesis outline:In the first part, we will introduce some basic knowledge about the linear mixed effect model and survival model, some algorithms used in the paper will also be intro-duced. In the second part, we will have a further introduction about the sub-models in joint model and the process of estimating parameters. In the third part, we will test the proposed method by numerical simulation which will be repeated 100 times. In this part, we will compare the results of the method we proposed with other methods. In the fourth part, we are going to do the example analysis and compare the results of different methods. The primary biliary cirrhosis data and the heart valve surgery data are used in this paper. In the final part, we will have a conclusion of the paper.